1. Field of Invention
This invention generally relates to teaching systems and more particularly to electronic teaching systems for teaching mathematics.
2. Prior Art
Students need to learn basic math facts such as elementary sums, differences, products, and quotients. The prior art contains many types of teaching systems designed to aid learning these facts.
The “Little Professor,” first produced by Texas Instruments in 1976, presented students with 16000 different arithmetic problems divided between the four basic math functions of addition, subtraction, multiplication, and division, and four different grade levels. The student could choose the function and level. The student was presented with problems like “3+5=?” If the answer was incorrect the child was presented with “EEE,” otherwise a new problem was given. Unfortunately, since students play little or no role in ascertaining the answer other than to provide it, they quickly become bored, necessitating extrinsic rewards to maintain their attention. Also, as others have reported, “Such devices do not provide information to assist the student in performing the solution and thus function best for students who have already mastered the material. Such devices perform more of a testing or review function than an instruction function,” Gill (1978).
The educational calculator disclosed in U.S. Pat. No. 4,126,949 to Simone (1978) requires a student to enter a problem and a supposed answer. The calculator then indicates, with a green or red light, the rectitude of the answer. “MATH MAGIC” introduced by Texas Instruments in 1977 functions in a similar manner, having the student enter the problem and the answer then indicating whether or not it was correct. These devices are an improvement because they promote activity by allowing the student to create the problems. However, they still suffer from the fact that a memorized answer is all that is called for and there is no instructional assistance.
Another teaching system is that disclosed in U.S. Pat. No. 4,114,294 to Marmer (1978). Marmer's device is essentially a calculator with delay circuitry allowing a student to guess an answer before the correct value is displayed. As stated in that disclosure, “the time competition stimulates and motivates the memorization of the proper answer.” This system is similar to Simone's except that there is a timing system meant to motivate the student. However, the student's role is still memorization and the student is still passive.
Another teaching system is that disclosed in U.S. Pat. No. 4,117,607 to Gill (1978). As noted above, Gill saw a need to provide assistance to the student as he/she is doing the problem. In Gill's invention assistance is provide two ways, by supplying carry/borrow information and by allowing students to check multi-step problems one step at a time. Although the type of device disclosed by Gill is theoretically more useful than that disclosed by Manner, the student is still required to memorize each individual step. In particular there is only one correct answer for each step and the student must provide it. There is no versatility in what the student is allowed to do. There are no individualized or idiosyncratic approaches to the problem allowed by this device. The creativity in an active student's mind is neither being utilized nor encouraged. Again, the student will quickly become bored.
An instructional calculator disclosed in U.S. Pat. No. 4,225,932 to Hirano et al. (1980) attempts to help students learn by displaying each step in the arithmetic process. The advantages and limitations of this calculator are similar to those of Gill (1978).
Another teaching device is disclosed in U.S. Pat. No. 5,139,423 to McCormick, et al. (1992). This device makes many different activities available to the student but the type of correct response for the individual activities is still just the single correct one. An additional feature of this device is its ability to graphically represent values and operations to the student, but these visuals do not enable the student to tailor different correct approaches to the answer.
Other teaching machines, such as disclosed in U.S. Pat. No. 4,611,996 to Stoner (1986), provide extrinsic rewards for correct answers. Stoner's device allows a student to play an electronic game following an adequate response. Though the stated intent of the game is to motivate the student, the side effect of extrinsic rewards is that students learn that math does not have value in and of itself. In addition, the method of presentation, similar to Simone's (1978), makes it more of a testing device than a training one.
Following in the belief that math must be made interesting with unrelated games, LeapFrog Enterprizes, Inc. has produced a number of devices. One of these is the Mind Mania™ Math Clip. Mind Mania™ Math Clip contains three games with three levels. Typical of the content of these games is Math Invaders, an arithmetic copy of the arcade game Space Invaders™, where students shoot down numbers instead of spaceships. Another device is Turbo Twist™ Math where the novelty is a twisting action to select numbers. Turbo Twist™ Math also has timed and multi-player modes to increase student interest. Yet another device is Electronic Flash Magic™ flash cards in which a flick of the wrist can be used to enter values or check answers. Again, these are truly testing devices more than training and the interest factor is external to the mathematics.
There have also been disclosed in the patent literature many mathematical puzzles and games designed to encourage learning through play thereby avoiding the boredom problem. Some puzzles, like U.S. Pat. No. 6,585,585 to Fletcher (2003), are quite popular on the internet, but treat numbers as characters in a puzzle with no mathematics other than the digits themselves.
The math manipulative educational learning game disclosed in U.S. Pat. No. 6,609,712 to Baumgartner (2003) is typical of a good non-electronic math game. Students learn mathematics in a manner which allows many different correct approaches to problems, thereby providing good outlets for creativity. The main limitation for games such as these is that the game requires a human partner with greater knowledge than the student. In Baumgartner's game this knowledgeable partner is called the Game Master. The game is not designed to be self teaching.
In addition to basic math facts students need to learn number sense. Number sense is “an awareness and understanding about what numbers are, their relationships, their magnitude, the relative effect of operating on numbers, including the use of mental mathematics and estimation,” (Fennel and Landis, 1994). There are no systems so far disclosed which specifically target number sense. The closest any disclosed method or device comes to teaching number sense is U.S. Pat. No. 5,638,308 to Stokes (1997). The disclosed device is a calculator with keys which can be selectively disabled. A student is presented with a math problem where one of the keys which would typically be used to solve the math problem has been disabled. The student must solve the problem by replacing the disabled key with a combination of the enabled keys and operations. Unfortunately there are a number of drawbacks to this system. Firstly, the level of mathematical sophistication required to use the device is often higher than the level of the number sense skill the device is attempting to reinforce. To quote from his disclosure, “As a very simple example, students may be instructed to disable the 8 key, then to solve the problem 8+18. The student can mentally factor each number in such a way as not to require use of the 8 key. The student thus arrives at (2.times.4)+(2.times.9). The student can use the distributive property to factor out the like 2's; 2.times.(4+9), which can be expressed as 2.times.13=26.” The number sense properties involving the “8” are much lower than the algebraic concepts of the distributive property. Secondly, with no disclosed system of hints or clues, there is inadequate feedback for a confused student. A student could be stuck on a problem for a long time and get quite frustrated. Lack of good feedback is a serious drawback when the goal is to get students to enjoy the process or to work independently. Thirdly, once a student found one way to replace a number, he/she may repeatedly use it and gain very little from additional problems. Additional problems become tedious and unproductive, another undesirable outcome. Fourthly, since the device is not a system of teaching math but merely a calculator, problems must still be separately provided by the teacher to the student. Poorly chosen problem sets would drastically reduce the effectiveness of the device. It is the set of problems chosen, much more than the device itself, which will determine its effectiveness. As a result, this device requires extensive teacher training to achieve the desired outcome.
Therefore a need has arisen for a teaching system which promotes an active role in learning, where the reward or satisfaction is intrinsic to the mathematics, and which helps students develop number sense.